# Single Image Super Resolution Technique: An Extension to True Color Images

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## Abstract

**:**

## 1. Introduction

^{2}(R

^{n}), the difference of the information in a signal at 2

^{i+1}and 2

^{i}resolution can be extracted [14]. There are extensive applications of wavelet analysis in every field of science (see [3] for an introduction). However, the computation of discrete wavelet transform of [14] involves sequential filtering operation. These filtering operations may also be executed using FFT [15], but the cost of computation of sequential process and the pyramid structure of [14] remains the same. The author of [16] claimed that his algorithm is parallel because the wavelet coefficients can be computed simultaneously.

## 2. Super-Resolution Techniques

## 3. Implementation

#### 3.1. Input RGB Image

#### 3.2. Channeling of Image

#### 3.3. Low-Resolution Image IL

#### 3.4. Up-Sampling Image IH(n)

Algorithm 1 Single super Image resolution algorithm |

Input: A true color image of 512 × 512 dimension |

Initialization: Channeling of input image to receive R, G, and B channels. |

Repeat 1 to 6 for I times |

1. Down-sampling of image in order to get the low-resolution image IL. |

2. Achieve the up-sampled image by using the up-sampling algorithm shown in Figure 2. |

3. Apply the Gaussian filter on the output came from step 2. |

4. Generate the down-sampled image IH_{down} |

5. Reconstruction error: Use the formula described in Equation (7) for the computation of reconstruction error |

6. Back Projection: Back projection is calculated using Equation (8). |

7. Combination of the three channels back to get the desired output. |

Output: Super-resolved image. |

_{i,j}= HH, HL, LH, LL and the value of threshold is computed by:

#### 3.5. Down-Sampling and Gaussain Filter

#### 3.6. UpSampling of the Error and Reconstruction

_{down}

#### 3.7. Back Projection Error

_{H}(n + 1) = E(n) + IH(n)

#### 3.8. Combining of the RGB Channel

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Original true color image: (

**a**) Einstein; (

**b**) Lena; (

**c**) Messi; (

**d**) baby; (

**e**) brain; (

**f**) baboon.

**Figure 7.**Super-resolved images using the proposed algorithm: (

**a**) Einstein; (

**b**) Lena; (

**c**) Messi; (

**d**) baby; (

**e**) brain; and(

**f**) baboon.

**Figure 8.**Bi-cubic interpolated images: (

**a**) Einstein; (

**b**) Lena; (

**c**) Messi; (

**d**) baby; (

**e**) brain; and (

**f**) baboon.

S. No | Test Images | PSNR | |
---|---|---|---|

Bi-cubic Interpolation | Proposed Method | ||

1 | Lena | 32.32 | 32.83 |

2 | Mona Lisa | 23.99 | 26.37 |

3 | Baboon | 24.12 | 28.37 |

4 | Einstein | 30.16 | 31.05 |

5 | Messi | 35.37 | 37.07 |

6 | Brain | 30.58 | 30.54 |

7 | Baby | 37.34 | 38.76 |

S. No | Test Images | PSNR | |
---|---|---|---|

Bi-cubic Interpolation | Proposed Method | ||

1 | Lena | 38.07 | 37.57 |

2 | Mona Lisa | 259 | 149 |

3 | Baboon | 251.2 | 94.5 |

4 | Einstein | 62.5 | 50.96 |

5 | Messi | 18.8 | 12.74 |

6 | Brain | 63.7 | 62.8 |

7 | Baby | 11.9 | 8.63 |

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**MDPI and ACS Style**

Irfan, M.A.; Khan, S.; Arif, A.; Khan, K.; Khaliq, A.; Memon, Z.A.; Ismail, M.
Single Image Super Resolution Technique: An Extension to True Color Images. *Symmetry* **2019**, *11*, 464.
https://doi.org/10.3390/sym11040464

**AMA Style**

Irfan MA, Khan S, Arif A, Khan K, Khaliq A, Memon ZA, Ismail M.
Single Image Super Resolution Technique: An Extension to True Color Images. *Symmetry*. 2019; 11(4):464.
https://doi.org/10.3390/sym11040464

**Chicago/Turabian Style**

Irfan, Muhammad Abeer, Sahib Khan, Arslan Arif, Khalil Khan, Aleem Khaliq, Zain Anwer Memon, and Muhammad Ismail.
2019. "Single Image Super Resolution Technique: An Extension to True Color Images" *Symmetry* 11, no. 4: 464.
https://doi.org/10.3390/sym11040464